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Re: mars and venus



First of all I'm relieved that what I said I understood about the outer
gas-ball planets and their prograde rotations, moon and ring orbits seems
to agree with what others also believe. *But* since it seems my claimed
expectation about the "normal" type of spin for inner planets formed by
gradual acretion (of small rocky bodies orbiting in a band of
protoplanetary material in essentially circular orbits) has met with much
dismay and disagreement on this list in that only John Mallinckrodt has
lent any fleeting confirmatory support (and even then, only after he ran
a single simulation), let me explain my reasoning for my claimed
expectation.

Consider a protoplanetary disk of small rocky bodies orbiting in nearly
circular orbits in a wide band around the Sun. The distribution of such
bodies is assumed to be polydisperse in mass. A few of the most massive
bodies exert a litle more attractive force on their neighbors than the
less massive ones do. Over time the massive bodies start accreting their
less massive neighbors and the disk is gradually (and probably unstably)
swept clean as the bodies build in size with the (mass) rich becoming
richer and the poor becoming poorer. Eventually what remains are only a
few objects that are widely spaced from each other that have separately
grown into the inner planets.

Now consider the situation midway through this scenario for a growing
planetoid/planetesimal, er whatever, (p/p for short) as it encounters
some less massive material on either (i.e. inner and outer) side of its
orbit. First consider the material that sweeps past the p/p on a
slightly smaller orbital radius. Since that material is in an inside
orbit it moves faster than the p/p and tends to encounter it from the
behind and inside as it passes by. Gravitational interactions with the
p/p act to tend to cause the material to be deflected toward the p/p
resulting in some accretory collisions. Since the material is incident
from the inside (i.e. sunward side) there will be a small bias in the
location of such collisions to be on the sunward (daylight) side of the
p/p. Since the collisions tend to come from behind as the accreting
matter is orbiting the Sun faster than the p/p is this causes the p/p to
experience a net angular impulse for a backward spin.

Now consider the material orbiting the Sun just outside the p/p. Now it
is the p/p that is orbiting faster than this other material and it (the
p/p) encounters that material from behind. This means that the forward
side of the p/p tends to get hit with the deflected material. But since
that material is coming from the outside (i.e. night) -- yet ahead side
of the p/p this means that the p/p will tend to suffer an excess of
collisions on its forward-night side and these collisions will *also*
tend to act to give the p/p a net angular impulse for a backward spin.
Essentially as the p/p orbits between the material on either side of it
that material tends to shear it from both sides in opposite directions
giving a net torque favoring a backward spin.

As the p/p accumulates matter it gradually acquires a net backward spin.
But since the bias toward which side of the p/p tends to experience
the most collisions from each side of the protoplanetary disk is
presumably small, this means that the p/p never gets much of a chance to
acquire a very large spin rate by the time it has swept clean its domain
of gravitational influence and stops growing. Thus the newly-grown
planet is left with a small backward rotation rate.

If this reasoning is all wet would someone explain where the error is?

David Bowman
dbowman@georgetowncollege.edu